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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

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The half-life of a radioactive nuclide is 100 hours ....

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:

(1) $\frac {1}{2}$                    (2) $\frac {1}{2\sqrt 2}$
(3) $\frac {2}{3}$                    (4) $\frac {2}{3\sqrt 2}$

Solution

Activity $A \propto N = \frac {N_0}{2^n}$

$A_0 \propto N_0 $

Fraction of original activity $\frac {A}{A_0}=\frac {1}{2^n}$, where n = number of half-lives

If half-life is 100 hours, number of half-lives in 150 hours = 1.5 = n

So, $\frac {A}{A_0}=\frac {1}{2^{1.5}}=\frac {1}{2\sqrt 2}$

Answer: (2)